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The distribution of prime ideals of imaginary quadratic fields |
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| Authors: | G. Harman A. Kumchev P. A. Lewis |
| Affiliation: | Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom ; Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3 ; School of Mathematics, Cardiff University, P.O. Box 926, Cardiff CF24 4YH, Wales, United Kingdom |
| Abstract: | Let  be a primitive positive definite quadratic form with integer coefficients. Then, for all  there exist  such that  is prime and  This is deduced from another result giving an estimate for the number of prime ideals in an ideal class of an imaginary quadratic number field that fall in a given sector and whose norm lies in a short interval. |
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